We will also use \(\operatorname{col}_r(G_\sigma )\)  and \(\operatorname{wcol}_r(G_\sigma )\)  to refer to the maximum \(r\) -reach over all vertices with respect to \(\sigma \) .
Under the given definitions, both of these parameters are closely linked with other important graph measures.
Specifically, \(\operatorname{col}_n(G) = tw(G)\)  [1]} and \(\operatorname{wcol}_n(G) = td(G)-1\)  [2]}.
Since \(\operatorname{col}_1(G) = \operatorname{wcol}_1(G) = \textit {deg}(G)\) , these parameters offer an interpolation between degeneracy and treewidth or tree-depth.
